Product integration for the linear transport equation in slab geometry

DOI10.1007/BF01398690zbMath0618.65143OpenAlexW4240760354MaRDI QIDQ1822476

Giovanni Monegato, Valentina Colombo

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133233

zbMATH Keywords

numerical examplesorder of convergenceNyström methodproduct quadrature rulelinear transport equation in slab geometryproduct Simpson rules

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Transport processes in time-dependent statistical mechanics (82C70)

Related Items (5)

Integral evaluation in the BEM solution of (hyper)singular integral equations. 2D problems on polygonal domains ⋮ A note on the convergence of product integration and Galerkin method for weakly singular integral equations ⋮ On the numerical resolution of the generalized airfoil equation with Possio kernel ⋮ Polynomial Approximations of Functions with Endpoint Singularities and Product Integration Formulas ⋮ Nyström-quasilinearization method and smoothing transformation for the numerical solution of nonlinear weakly singular Fredholm integral equations

Cites Work

• Analysis of general quadrature methods for integral equations of the second kind
• Adjoining appropriate singular elements to transport theory computations
• Formulation of a Ritz-Galerkin type procedure for the approximate solution of the neutron transport equation
• Eigenvectors of certain matrices
• Integral equation methods for transport problems. Some numerical results
• Asymptotic Error Bounds for a Class of Interpolatory Quadratures
• On the Differential Properties of Solutions to Fredholm Equations with Weakly Singular Kernels
• Product-Integration Rules Based on the Zeros of Jacobi Polynomials
• A Fast Galerkin Algorithm for Singular Integral Equations
• Product Integration for Weakly Singular Integral Equations
• A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel
• Galerkin Methods for Second Kind Integral Equations with Singularities
• Asymptotic Behavior of the Solution of the Integral Transport Equation in Slab Geometry
• Continuity and Differentiability Properties of the Solution of the Linear Transport Equation
• Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function
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